by Qev » Sun Dec 16, 2007 5:48 pm
Entropy can be used as a measurement for the amount of information a system can hold. Quantum-mechanically, a black hole is maximally entropic: no region of space can contain more entropy than a black hole that fills that space. The amount of entropy increases with increasing mass. The surface area of a black hole is proportional to its mass. Therefore the information content of the volume enclosed by a black hole is determined not by the volume, but by the surface area of the boundary.
At least, that's my rather simplified understanding of it. It leads to the peculiarities of the Strong and Weak Holographic Principles; the Weak is especially strange. Basically, anything occurring in any volume of space can be made exactly equivalent to its two-dimensional representation on the enclosing surface area... making 'volume' an illusion.
I love the Holographic Principle... it's just so mind-twisting, and the math backs it up, which makes it even more mind-twisting.
The image in the APOD obviously
isn't a hologram, since those don't work on a computer screen, so it's 'the next nearest thing', a random dot autostereogram. They actually
can be animated, though those are more difficult to view properly. I seem to recall one of a
swimming shark.
Entropy can be used as a measurement for the amount of information a system can hold. Quantum-mechanically, a black hole is maximally entropic: no region of space can contain more entropy than a black hole that fills that space. The amount of entropy increases with increasing mass. The surface area of a black hole is proportional to its mass. Therefore the information content of the volume enclosed by a black hole is determined not by the volume, but by the surface area of the boundary.
At least, that's my rather simplified understanding of it. It leads to the peculiarities of the Strong and Weak Holographic Principles; the Weak is especially strange. Basically, anything occurring in any volume of space can be made exactly equivalent to its two-dimensional representation on the enclosing surface area... making 'volume' an illusion. :lol:
I love the Holographic Principle... it's just so mind-twisting, and the math backs it up, which makes it even more mind-twisting. :D
The image in the APOD obviously [b]isn't[/b] a hologram, since those don't work on a computer screen, so it's 'the next nearest thing', a random dot autostereogram. They actually [b]can[/b] be animated, though those are more difficult to view properly. I seem to recall one of a [url=http://en.wikipedia.org/wiki/Image:Stereogram_Tut_Animated_Shark.gif]swimming shark[/url].